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3 years ago

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Mathematics

1 answer:

SIZIF [17.4K]3 years ago

3 0

Answer:

facts

Step-by-step explanation:

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A piece of wire of length L will be cut into two pieces, one piece to form a square and the other piece to form an equilateral t

inn [45]

Answer:

(a) square: L; triangle: 0.

(b) square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11

Step-by-step explanation:

<u>Strategy</u>: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.

In terms of its perimeter p, the area of a square is ...

A_square = p^2/16

In terms of its perimeter p, the area of an equilateral triangle is ...

A_triangle = p^2/(12√3)

Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...

A_total = x^2/16 + (L-x)^2/(12√3)

(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.

(b) The derivative of A_total with respect to x is ...

dA/dx = x/8 -(L-x)/(6√3)

This will be zero when ...

x/8 = (L-x)/(6√3)

x(6√3) = 8L -8x

x(8 +6√3) = 8L

x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)

x = L·(12√3 -16)/11

The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.

5 0

3 years ago

Janalyn Cooper's gross weekly pay is $798. Her earnings to date for the year total $11,970.

myrzilka [38]

Answer:

$2000 I hope it's helpful for you

8 0

3 years ago

Kevin plans to put concrete on a rectangular portion of his driveway. The portion is 10 feet long and 3 inches high. The price o

Elis [28]

We are given the dimensions 10 feet length and 3 inches height. The volume of the rectangular portion is equal to $72.59 / $98 per cubic yard that is equal to 0.74 cubic yard. This is equal to 19.98 cubic feet. This means the width of the portion is equal to 8 feet.

3 0

3 years ago

Read 2 more answers

PLEASEEE HELPPPP ASAPPPP

stellarik [79]

$\cos 27^{\circ} = \dfrac{KL}x\\\\\implies \cos 27^{\circ} = \dfrac{6.3}x\\\\\implies x = \dfrac{6.3}{\cos 27^{\circ}}=7.1~ \text{units.}$

6 0

2 years ago

One more time!

CaHeK987 [17]

Since q(x) is inside p(x), find the x-value that results in q(x) = 1/4

$\frac{1}{4} = 5 - x^2\ \Rightarrow\ x^2 = 5 - \frac{1}{4}\ \Rightarrow\ x^2 = \frac{19}{4}\ \Rightarrow \\
x = \frac{\sqrt{19} }{2}$

so we conclude that
$q(\frac{\sqrt{19} }{2} ) = 1/4$

therefore

$p(1/4) = p\left( q\left(\frac{ \sqrt{19} }{2} \right) \right)$

plug $x=\sqrt{19}/2$ into p( q(x) ) to get answer

$p(1/4) = p\left( q\left( \frac{ \sqrt{19} }{2} \right) \right)\ \Rightarrow\ \dfrac{4 - \left( \frac{\sqrt{19} }{2}\right)^2 }{ \left( \frac{\sqrt{19} }{2}\right)^3 } \Rightarrow \\ \\ \dfrac{4 - \frac{19}{4} }{ \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{8\left(4 - \frac{19}{4}\right) }{ 8 \cdot \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{32 - 38}{19\sqrt{19}} \Rightarrow \dfrac{-6}{19\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}\Rightarrow$

$\dfrac{-6\sqrt{19} }{19 \cdot 19} \\ \\ \Rightarrow -\dfrac{6\sqrt{19} }{361}$

$p(1/4) = -\dfrac{6\sqrt{19} }{361}$

3 0

3 years ago